[Kilojoule.kJ]

Hi Guys! So I am having problem to assess the concept between the two Problems below:

Problem 1: A 0.500 g sample of TNT (C7H5N2O6) is burned in a bomb calorimeter containing 610 grams of water at an initial temperature of 20.00°C. The heat capacity of the calorimeter is 420 J/°C and the heat of combustion of TNT is 3374 kJ/mol. Using these data, calculate the final temperature of the water and calorimeter once the reaction is complete.

In Problem 1: The formula used is Q_rxn = Q_water + Q_cal, and the answer is 23°C

Problem 2: A 30.14-g stainless steel ball bearing at 117.82°C is placed in a constant-pressure calorimeter containing 120.0 mL of water at 18.44C. If the specific heat of the ball bearing is 0.474 J/g°C, calculate the final temperature of the water. Assume the calorimeter to have negligible heat capacity.

In Problem 2: The formula uses is Q_rxn = - Q_water, and the answer is 21°C

Question is, why did in Problem the formula does not show a negative sign to indicate the direction of heat flow, andd in Problem 2 it does when they are both calorimetry problems and involved solving for the final temperature? Any help is appreciated. Thank you!

[Hunter2]

In the first example you have an increasing of temperature during combustion.
In the second one you have a decrease of temperature of the ball by placing it into the water.

[Borek]

Question is, why did in Problem the formula does not show a negative sign to indicate the direction of heat flow

You sum heats, these heats can have a negative or positive sign, depending on whether the part of the system absorbs or gives heat. This way for every part of the system you use exactly same the same formula mc(T_final-T_initial) and you don't need to play with signs, which is a sure way of confusing something at some point.